A newly married couple does not want to get pregnant during their first year of marriage and decides to only use condoms as a contraceptive device.

A newly married couple does not want to get pregnant during their first year of marriage and decides to only use condoms as a contraceptive device. Studies1 have shown that the probability of pregnancy per use of a condom is 0.15% (individual probability of pregnancy). During the first year the couple use a condom every time for a total of 162 times.

Would it be unusual to become pregnant during 1 year of use when only using this form of contraceptive?

Given that, the probability of pregnancy during their first year of marriage is,

P= 0.15%= 0.0015

The number of times that a condom was used is

n= 162

Let X: the number of times of getting pregnant per use of a condom.

Here, X~Binom(n=162,P=0.0015)

In this situation, we use binomial to normal approximation, because n is large and p tends to 0.

The parameters of normal distribution is,

μ = n`\times`P= 162`\times`0.0015 = 0.243

σ = √(n`\times`P`\times`(1-P)= √[162`\times`0.0015`\times`(1-0.0015)]

σ = √0.24264 = 0.4926

The probability of 1 or more pregnancies over 1 year is,

P(X≥1) = P((X-μ) / σ ≥ (1-0.243) / 0.4926)

P(X≥1) = P(Z ≥ 1.5368)

From the normal table,

P(Z≥ 1.5368) = 0.0622

Generally, the z-scores lower than -1.96 or higher than 1.96 are considered unusual.

Here, z-score corresponding to X = 1 is,

z = `"(X-μ)"/"σ"`

z = `"(1-0.243)"/"0.4926"`

z = 1.5368 which lies between -1.96 and 1.96.

As a result, it will not be unusual to become pregnant during 1 year.